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More Connected Capacitors

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  1. Mar 26, 2015 #1
    1. The problem statement, all variables and given/known data
    Capacitors ## C_1 = 4 \mu F## and ##C_2 = 2 \mu F## are charged as a series combination across a ## 100V## battery. The two capacitors are disconnected from the battery and from each other. They are then connected positive plate to positive plate and negative plate to negative plate. Calculate the resulting charge on each capacitor.

    2. Relevant equations
    ##C = \frac{Q}{V} ##
    Parallel: Same Voltage
    Series: Same Charge

    3. The attempt at a solution
    Is this correct:

    Since the two capacitors are connected in series, their resulting capacitance is ##\frac{4}{3} \mu F##, so the charge on each capacitor is ## 133.33 \mu C##; therefore, when they are connected pos. to pos. and neg. to neg., both charges will be ##133.33 \mu C##.
     
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  3. Mar 26, 2015 #2

    gneill

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    The capacitors are of different size so with the same initial charge they will have different voltages. When they are then connected in parallel as described, the voltage difference must be reconciled by charges moving to eliminate the potential differences. But total charge must be conserved...
     
  4. Mar 26, 2015 #3
    How do you know they are "connected in parallel as described": I thought it's series?
     
  5. Mar 26, 2015 #4

    gneill

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    The problem statement says: "They are then connected positive plate to positive plate and negative plate to negative plate."
     
  6. Mar 26, 2015 #5
    How do you know that is parallel?
     
  7. Mar 26, 2015 #6

    gneill

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    Technically you can interpret the result as either series or parallel connection since it satisfies both definitions. But in this case it's convenient to look at the connection as being parallel so that you can take advantage of the fact that parallel components share the same potential difference.
     
  8. Mar 27, 2015 #7
    No, you cannot look at the connection as being series, because the charge is not the same...
     
  9. Mar 27, 2015 #8

    ehild

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    In case of series capacitors, the charges on the connected plates are of equal magnitude, but of opposite sign so the net charge of the connected plates is zero. In this case, they are of the same sign, .
     
    Last edited: Mar 27, 2015
  10. Mar 27, 2015 #9

    SammyS

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    The above exchange strikes me as being rather odd.
     
  11. Mar 27, 2015 #10

    gneill

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    Series vs parallel is a matter of physical connection topology. How charge distribution behaves when the pair is connected to an external source is another matter (related, but not defining).
     
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